Constructive Quantum Field Theory

该项目的目的是构建和研究数学上精确的量子场论模型。 更广泛的目标是加深我们对量子场论的理解，提高其预测能力，从而加深我们对基本粒子物理和统计力学中临界现象的理解。 该项目特别强调重整化群。 这是一种广泛适用于分析空间或时间中渐近行为的方法，另一个广泛的目标是使重整化群技术更精确，更系统，更易于使用。 具体项目目标是：（1）重整化群的非高斯不动点的构造，以及相关的反常临界指数的研究，（2）在三维时空中量子电动力学和/或非阿贝尔规范理论的构建，以及（3）模拟非阿贝尔规范理论的标量模型中质量产生的研究。

The purpose of the project is to construct and study mathematically precise quantum field theory models. The broader goal is sharpen our understanding of quantum field theory and increase its predictive power, thereby deepening our understanding of elementary particle physics and critical phenomena in statistical mechanics. The project particularly emphasizes the renormalization group. This is a widely applicable method for analyzing asymptotic behavior in space or time, and another broad goal is to make renormalization group techniques more precise, systematic, and easy to use. Specific project goals are: (1.) the construction of non-Gaussian fixed points for the renormalization group, and a study of the associated anomalous critical exponents, (2.) the construction of quantum electrodynamics and/or non-Abelian gauge theories in three space-time dimensions, and (3.) the study of mass generation in a scalar model simulating non-Abelian gauge theories.